Voting with Preference Intensities

When an agent votes, she typically ranks the set of available alternatives. Occasionally, she may also wish to report the intensity of her preferences by indicating adjacent pairs of alternatives in her ranking between which her preference is acutely decisive; for instance, she may suggest that she likes alternative a more than b, but b much more than c. We design near-optimal voting rules which aggregate such preference rankings with intensities using the recently-popular distortion framework. We also show that traditional voting rules, which aggregate preference rankings while ignoring (or not eliciting) intensities, can incur significant welfare loss.